0,1

A homeomorphically irreducible general graph is a graph with multiple edges and loops and without nodes of degree 2.

I. P. Goulden and D. M. Jackson, Combinatorial Enumeration, Wiley, N.Y., 1983.

V. Jovovic, Generating functions for homeomorphically irreducible general graphs on n labeled nodes

V. Jovovic, Recurrences for the numbers of homeomorphically irreducible general graphs on m labeled nodes and n edges

G.f.: (x^2 - x + 1)/(1 - x). a(0)=1, a(1)=0, a(n)=1, n>1.

E.g.f. for homeomorphically irreducible general graphs with n nodes and k edges is (1 + x*y)^(- 1/2)*exp(- x*y/2 + x^2*y^2/4)*Sum_{k >= 0} 1/(1 - x)^binomial(k + 1, 2)*exp(- x^2*y*k^2/(2*(1 + x*y)) - x^2*y*k/2)*y^k/k!.

E.g.f.: e^x-x; - Paul Barry (pbarry(AT)wit.ie), May 06 2007

a(n)=1-C(1,n)+C(0,n), with n>=0 - Paolo P. Lava (ppl(AT)spl.at), Feb 15 2008

Cf. A003514, A060516, A060533-A060537, A060577-A060581.

Adjacent sequences: A060573 A060574 A060575 this_sequence A060577 A060578 A060579

Sequence in context: A131695 A105812 A134323 this_sequence A019590 A014040 A014071

nonn

Vladeta Jovovic (vladeta(AT)Eunet.yu), Apr 03 2001